Align internal face of UV island with another island
Using Snap to vertices in the UV editor is really the only option you have for aligning. 
Select the parts you want to move, and move the cursor over them until they snap to the side you want. This should work fine with more complex unwraps too.

I verified this by testing it out on a suzanne head here:



After:



This is about the closest you can get to actually aligning faces, other than eyeballing it.